An adaptive scheme for the approximation of dissipative systems
Probability
2018-02-20 v1
Abstract
We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit Euler scheme are CPU-time expensive. The algorithm we introduce is explicit and we prove that any weak limit of the weighted empirical measures of this scheme is a stationary distribution of the stochastic differential equation. Several examples are presented including gradient dissipative systems and Hamiltonian dissipative systems.
Cite
@article{arxiv.math/0502317,
title = {An adaptive scheme for the approximation of dissipative systems},
author = {Vincent Lemaire},
journal= {arXiv preprint arXiv:math/0502317},
year = {2018}
}